Linear Equations and Inequalities: Free Course

About this course

Equations and inequalities describe constraints on unknown quantities. This course develops one-step and multistep solutions, proportions, variation and algebraic word problems. Study the complete public source playlist from Khan Academy in English, with all 35 recordings in the on-site classroom. Original lesson titles, source order and repeated entries are preserved.

Course at a glance

What you’ll learn

• Solve one-step and multistep linear equations.
• Solve inequalities while preserving their meaning.
• Translate ratio and proportion problems into equations.
• Distinguish direct and inverse variation.

Skills you’ll gain

• Linear equations
• Inequalities
• Proportions
• Variation

Course Overview

Balance-preserving steps connect simple equations with examples containing variables on both sides. The inequality recordings examine what happens when multiplying or dividing, including the change in comparison direction when the factor is negative. Proportion problems connect ratios with equations, and direct and inverse variation add relationships between changing quantities. Contextual examples require defining an unknown and translating the statement before solving. A candidate answer should satisfy the original condition, not only an intermediate rearrangement. For an inequality, the result is usually a set of allowed values, so explain its meaning in the situation rather than reporting only a boundary number.

How to study the course

• Videos 1–8: this part of the source list includes “One-step inequality involving addition” through “Constructing equations from proportions to solve problems”. State the quantities and conditions before calculating. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 9–17: this part of the source list includes “Example 1: Variables on both sides” through “Figuring out missing algebraic step”. Keep equivalent expressions or representations connected. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 18–26: this part of the source list includes “Multi-step inequalities 3” through “Introduction to solving an equation with variables on both sides”. Check each operation with a small example before extending it. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.
• Videos 27–35: this part of the source list includes “Word problem: solving equations” through “Solving a two-step inequality”. Explain a result in words as well as symbols. Keep a brief working note, revisit an unclear explanation and test one example before moving to another part of the material.

Who is this for?

This course suits students, returning learners and anyone strengthening the specific mathematics named in the course. It also provides a recorded reference for revisiting a topic after an earlier lesson or study attempt. Choose examples appropriate to your background and allow time to work through the method instead of judging understanding only by how familiar the terminology sounds.

Before you start

Comfort with the preceding arithmetic or algebra skills is useful. Keep paper, a pencil and a calculator when a lesson uses one. Grade-specific courses assume the learner’s earlier grade-level knowledge.

Put the lessons into practice

Write a fictional budget inequality and solve for the allowed number of items. Interpret whole-number restrictions separately from the algebraic boundary. Solve a variables-on-both-sides equation and substitute the result into the original statement. Compare a direct-variation table with an inverse-variation table and identify the constant relationship in each.

This optional study activity is provided by WikiFree for independent practice. Keep your working notes and use the relevant classroom recording to check a step, definition or interpretation. It is not an instructor-marked assignment.

Certificate / Assessment

Watching the public videos and using WikiFree completion tracking does not award a certificate, academic credit, an examination voucher or instructor assessment. Use your practice output to review what you can explain and repeat independently. The recorded lessons provide study material; completion tracking records your progress through that material.

Frequently asked questions

Provider: Khan Academy. Videos play from the Khan Academy channel on YouTube.